Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis

Abstract

We develop a combined coupled-cluster (CC) or equation-of-motion coupled-cluster (EOM-CC) theory and Rayleigh–Schrödinger perturbation theory on the basis of a perturbation expansion of the similarity-transformed Hamiltonian H̄=exp(−T)H exp(T). This theory generates a series of perturbative corrections to any of the complete CC or EOM-CC models and hence a hierarchy of the methods designated by CC(m)PT(n) or EOM-CC(m)PT(n). These methods systematically approach full configuration interaction (FCI) as the perturbation order (n) increases and/or as the cluster and linear excitation operators become closer to complete (m increases), while maintaining the orbital-invariance property and size extensivity of CC at any perturbation order, but not the size intensivity of EOM-CC. We implement the entire hierarchy of CC(m)PT(n) and EOM-CC(m)PT(n) into a determinantal program capable of computing their energies and wave functions for any given pair of m and n. With this program, we perform CC(m)PT(n) and EOM-CC(m)PT(n) calculations of the ground-state energies and vertical excitation energies of selected small molecules for all possible values of m and 0⩽n⩽5. When the Hartree–Fock determinant is dominant in the FCI wave function, the second-order correction to CCSD [CC(2)PT(2)] reduces the differences in the ground-state energy between CCSD and FCI by more than a factor of 10, and thereby significantly outperforms CCSD(T) or even CCSDT. The third-order correction to CCSD [CC(2)PT(3)] further diminishes the energy difference between CC(2)PT(2) and FCI and its performance parallels that of some CCSD(TQ) models. CC(m)PT(n) for the ground state with some multideterminantal character and EOM-CC(m)PT(n) for the excitation energies, however, appear to be rather slowly convergent with respect to n.